Accurate solutions of distributed parameter systems may be represented as the sum of an infinite series. Control design however, requires low-order models primarily due to implementation limitations. As such, developing low-order models of high fidelity is important if the objective is accurate control of the DPS. This work addresses this issue by developing a method that assures a convergent and consistent projection to a finite space. The resulting model is then subsequently used to design finite dimensional state feedback controllers. The methodology is demonstrated on two quasi-linear processes under ideal and non-ideal conditions.